Variance Reduction in Gibbs Sampler Using Quasi Random Numbers

Abstract A sequence of s-dimensional quasi random numbers fills the unit cube evenly at a much faster rate than a sequence of pseudo uniform deviates does. It has been successfully used in many Monte Carlo problems to speed up the convergence. Direct use of a sequence of quasi random numbers, however, does not work in Gibbs samplers because the successive draws are now dependent. We develop a quasi random Gibbs algorithm in which a randomly permuted quasi random sequence is used in place of a sequence of pseudo deviates. One layer of unnecessary variation in the Gibbs sample is eliminated. A simulation study with three examples shows that the proposed quasi random algorithm provides much tighter estimates of the quantiles of the stationary distribution and is about 4–25 times as efficient as the pseudo algorithm. No rigorous theoretical justification for the quasi random algorithm, however, is available at this point.

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